MOSUL, Iraq (Reuters) - Mohammed Ali and his family, carrying all their worldly possessions in a few bags, had been on the road for 18 hours since fleeing their home in an Islamic State-held area of Mosul.

They hoped to find shelter at a camp. So far, they have had no luck.

"We tried at Hammam al-Alil camp," about 35 km (22 miles) south of Mosul, the 50-year-old said, flanked by 20 relatives including sons and grand-nephews and nieces. "It was full."

A bus had brought them from there and unloaded them a few hundred metres (yards) from a Kurdish peshmerga checkpoint east of Mosul and on the way to the sprawling Khazer and Hasan Sham camps, which are also crowded.

"Hopefully we can get to Khazer. We just need to get through the checkpoint," Ali said.

Ali's story is becoming a familiar one.

Displaced Iraqis are streaming out of western Mosul at a quickening pace as fighting intensifies in the city. They are arriving at camps to find there is no room, forced to get back onto buses or hire taxis to reach other areas.

Some head for new camps being built to try to cope with the exodus, but with poor living conditions, many western Mosul residents make instead for the east side of the city, which was recaptured from Islamic State in January, to stay with relatives or find shelter in half-finished buildings.

The U.S.-backed Iraqi offensive to drive Islamic State out of Mosul, their last major stronghold in the country, has confined the jihadists to about half of the western side.

Iraq's immigration minister, Jassim Mohammed, said on Monday the number of displaced people from both sides of the city since the start of the campaign had reached 355,000.

The United Nations refugee agency (UNHCR) recently opened a new camp that filled up within a week and is building another in Hammam al-Alil to received thousands more families.

Hammam al-Alil has become the main transit point for the Mosul displaced. At the current camp's main entrance, hundreds of Iraqis wait in the mud and cold, crouching by small fires, using porta-cabin toilets and asking which buses will take them onwards.

Taxi drivers tout for business, many shouting "Mosul, Mosul!" – to take people back to the eastern side of the city.

SHELTER IN EAST

Eastern Mosul is a preferable destination for many who have relatives there.

"In the rubble there is nothing. If there is water maybe we will go back. We're heading to the east we have family. We can't stay in those camps," Bushra Mohammed Ali, who left the west with his sister and two daughters, said on Monday.

A woman named Um Tahseen, who had fled the Jidida district, said her family had gone 11 days without food.

"The militants, they beat people they don't like or kill them. Why would we go to the camps and face more hardships there. We will go to the east. Maybe there is no water there either but a least we have family."

In the centre of eastern Mosul on Sunday, many young men wandering through a market said they were from western Mosul, crammed into homes with anywhere from seven to 15 relatives with whom they had fled.

Outside the Nabi Yunus shrine, 30-year-old Waddah, who had fled the Islamic State-held Old City in the west with his two wives, two children and his brother's family, worked shovelling debris into a skip.

"I came to stay with my cousin in Sumer district," he said.

"It's not ideal - we're 15 people cramming into his home and into an out-house - but it's better than being in the cold, crowded camps," Waddah said.

More than anything Waddah was relieved to have escaped Islamic State but he was worried for family still trapped inside the west. He gave only his first name for fear they would be identified.

"My brother is there. He tries to call when he can, using a phone from his cellar," he said. Islamic State militants threaten those caught using mobile phones with death.

"I'm scared for my family still inside. They don’t call every day because they can't. Every time they don’t, I worry that something has happened to them."

(Reporting by John Davison and Patrick Markey, Editing by Angus MacSwan and Andrew Heavens)